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Published on: 29/10/2025
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1.
If \({ x }^{ \frac { 1 }{ 12 } }={ 49 }^{ \frac { 1 }{ 24 } }\), then x is equal to:
49
2
12
7
2.
The value of \(\sqrt [ 4 ]{ \sqrt [ 3 ]{ { 2 }^{ 2 } } } \) is equal to:
\({ 2 }^{ -\frac { 1 }{ 6 } }\)
\({ 2 }^{ -6 }\)
\({ 2 }^{ \frac { 1 }{ 6 } }\)
\({ 2 }^{ 6 }\)
3.
The simplified form of \(\frac { { 13 }^{ \frac { 1 }{ 5 } } }{ { 13 }^{ \frac { 1 }{ 3 } } } \) is
\({ 13 }^{ \frac { 2 }{ 15 } }\)
\({ 13 }^{ \frac { 8 }{ 15 } }\)
\({ 13 }^{ \frac { 1 }{ 3 } }\)
\({ 13 }^{ \frac { 2 }{ 15 } }\)
4.
(0.001)1/3 is equal to
0.1
0.001
0.01
0.0001
5.
\(\sqrt [ 3 ]{ \frac { 54 }{ 250 } } \) equals:
\(\frac { 9 }{ 25 } \)
\(\frac { 3 }{ 5 } \)
\(\frac { 27 }{ 125 } \)
\(\frac { \sqrt [ 3 ]{ 2 } }{ 5 } \)
6.
The simplified value of \({ \left( 81 \right) }^{ -1/4 }\times \sqrt [ 4 ]{ 81 } \) is:
9
3
1
0
7.
Simplified value of \({ \left( 16 \right) }^{ \frac { 1 }{ 4 } }\times \sqrt [ 4 ]{ 16 } \) is:
16
4
1
0
8.
The value of \(\sqrt [ 4 ]{ { \left( 64 \right) }^{ -2 } } \) is
1/8
1/2
8
1/64
9.
The value of \(\sqrt { \left( { 3 }^{ -2 } \right) } \)
1/9
9
-3
1/3
10.
Simplified value of \({ \left( 25 \right) }^{ \frac { 1 }{ 3 } }\times { \left( 5 \right) }^{ \frac { 1 }{ 3 } }\) is:
25
3
1
5
11.
The value of \(\sqrt [ 3 ]{ 216 } -\sqrt [ 3 ]{ 125 } \) is:
1
0
2
-1
12.
The value of \({ \left( 243 \right) }^{ \frac { 1 }{ 3 } }\) is equal to:
5
3
6
1
13.
When \(15\sqrt { 5 } \) is divided by \(3\sqrt { 3 } \) , the quotient is:
\(5\sqrt { 3 } \)
\(3\sqrt { 5 } \)
\(5\sqrt { 5 } \)
\(3\sqrt { 3 } \)
14.
If \({ x }^{ a/b }=1,\)then the value of a is
0
1
-1
None of these
15.
The value of \(\frac { { 2 }^{ 0 }\times { 7 }^{ 0 } }{ { 5 }^{ 0 } } \) is:
1
0
9/5
1/5
16.
If a = 2 and b = 3, then the value of ba is
4
9
2
3
17.
If b>0 and b2=a then \(\sqrt { a } \) is equal to:
-b
b
\(\sqrt { b } \)
b2
18.
Rationalization of the denominator of \(\frac { 1 }{ \sqrt { 5 } +\sqrt { 2 } } \) gives:
\(\frac { 1 }{ \sqrt { 10 } } \)
\(\sqrt { 5 } +\sqrt { 2 } \)
\(\sqrt { 5 } -\sqrt { 2 } \)
\(\frac { \left( \sqrt { 5 } -\sqrt { 2 } \right) }{ 3 } \)
19.
If \(\sqrt { 3 } =1.732\) and \(\sqrt { 2 } =1.414\) , the value of \(\frac { 1 }{ \sqrt { 3 } -\sqrt { 2 } } \) is:
0.318
3.146
1/3.146
\(\sqrt { 1.732 } -\sqrt { 1.414 } \)
20.
Value of \(\frac { 1 }{ \sqrt { 18 } -\sqrt { 32 } } \) is equal to:
\(\sqrt { 2 } \)
\(-\sqrt { 2 } \)
\(\frac { 1 }{ \sqrt { 2 } } \)
\(-\frac { 1 }{ \sqrt { 2 } } \)
21.
\(\sqrt { 12 } \times \sqrt { 18 } \) is equal to:
\(2\sqrt { 6 } \)
\(3\sqrt { 6 } \)
\(4\sqrt { 6 } \)
\(6\sqrt { 6 } \)
22.
\({ \left( \sqrt { 2 } +1/\sqrt { 2 } \right) }^{ 2 }\) is equal to:
\(4\sqrt { 2 } \)
9/2
\(4/\sqrt { 12 } \)
9
23.
If \(x=\frac { \sqrt { 7 } }{ 5 } \) and \(\frac { 5 }{ x } =p\sqrt { 7 } \) , then the value of p is:
\(\frac { 5 }{ \sqrt { 7 } } \)
\(\frac { 25 }{ 7 } \)
\(\frac { 7 }{ 25 } \)
\(\frac { \sqrt { 7 } }{ 5 } \)
24.
\(\left( 5+\sqrt { 8 } \right) +\left( 3-\sqrt { 2 } \right) -\left( \sqrt { 2 } -6 \right) \) when simplified is:
positive and irrational
negative and irrational
positive and rational
negative and rational
25.
\(\left( -2-\sqrt { 3 } \right) \left( -2+\sqrt { 3 } \right) \) when simplified is:
positive and irrational
positive and rational
negative and irrational
negative and rational
26.
Which of the following numbers is an irrational number?
\(\sqrt { 16 } -4\)
\(\left( 3-\sqrt { 3 } \right) \left( 3+\sqrt { 3 } \right) \)
\(\sqrt { 5 } +3\)
\(-\sqrt { 25 } \)
27.
\(\left( a+\sqrt { b } \right) \left( a-\sqrt { b } \right) \) is equal to:
\({ b }^{ 2 }-{ a }^{ 2 }\)
\({ a }^{ 2 }-{ b }^{ 2 }\)
\({ a }^{ 2 }-b\)
\({ b }^{ 2 }-a\)
28.
\(\left( \sqrt { a } +\sqrt { b } \right) \left( \sqrt { a } -\sqrt { b } \right) \) is:
a+b
a-b
\(2\sqrt { a } \)
\(2\sqrt { b } \)
29.
The sum of \(0.\overline { 3 } \) and \(0.\overline { 2 } \)
\(\frac { 5 }{ 99 } \)
\(\frac { 5 }{ 9 } \)
\(\frac { 5 }{ 10 } \)
\(\frac { 5 }{ 100 } \)
30.
The value of \(2.\overline { 9 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\), is
\(\frac { 2999 }{ 1000 } \)
\(\frac { 19 }{ 10 } \)
3
\(\frac { 26 }{ 9 } \)
31.
An irrational number between \(\frac { 5 }{ 7 } \) and \(\frac { 7 }{ 9 } \)
0.75
\(\sqrt { 6 } \)
0.750 7500 75000...
0.7512
32.
\(\pi \) is:
a rational number
an integer
an irrational number
a whole number
33.
The decimal expansion of \(\sqrt { 2 } \) is
finite decimal
1.4121
non-terminating recurring
non-terminating non-recurring
34.
Which of the following is an irrational number?
\(3.\overline { 3 } \)
3.763
\(3.\overline { 763 } \)
3.101 1001 10001...
35.
Which of the following numbers is an irrational number?
\(\sqrt { 23 } \)
\(\sqrt { 225 } \)
0.3796
\(7.\overline { 478 } \)
36.
Which of the following is an irrational number?
0.15
\(0.15\overline { 16 } \)
\(0.\overline { 1516 } \)
0.501 5001 50001...
37.
\(5.3\overline { 7 } \) lies most accurately
between 5.37 and 5.38
between 5.3 and 5.4
between 5.377 and 3.378
between 5.3777 and 5.3778
38.
The process of visualisation of representation of numbers on the number line through a magnifying glass is called
successive magnification
approximation
imagination
none of these
39.
Which one of the following is an irrational number?
0.14
\(0.\overline { 1416 } \)
\(0.\overline { 1416 } \)
0.401 4001 40001 4...
40.
Which of the following is a rational number?
\(\sqrt { 5 } \)
\(\pi \)
0.101 001 0001 00001...
0.853 853 853....
41.
A number is an irrational if and only if its decimal representation is:
non-terminating
non-terminating and repeating
non terminating and non repeating
terminating
42.
A terminating decimal is:
natural number
a whole number
a rational number
an integer
43.
The decimal form of 56/1000 is
0.56
0.056
0.0056
5.6
44.
If \(\sqrt { x } \) is an irrational number, then x is:
rational
irrational
0
real
45.
Two rational numbers between \(\frac { 2 }{ 3 } \) and \(\frac { 5 }{ 3 } \)are:
1/6 and 2/6
1/2 and 2/7
5/6 and 7/6
2/3 and 4/3
46.
The rational number between -1/5 and -2/5 is
0
-1/4
-3/10
-7/25
47.
A rational number lying between \(\sqrt { 2 } \) and \(\sqrt { 3 } \) is:
\(\frac { \sqrt { 2 } +\sqrt { 3 } }{ 2 } \)
\(\sqrt { 6 } \)
1.6
1.9
48.
A rational number lying between -3 and 3 is:
0
-4.3
-3.4
1.101 1001 10001...
49.
Every rational number is:
a natural number
an integer
a real number
a whole number
50.
Which of the following is a rational number?
\(1+\sqrt { 3 } \)
\(\pi \)
\(2\sqrt { 3 } \)
0
1.
(d)
7
2.
(c)
\({ 2 }^{ \frac { 1 }{ 6 } }\)
3.
(d)
\({ 13 }^{ \frac { 2 }{ 15 } }\)
4.
(a)
0.1
5.
(b)
\(\frac { 3 }{ 5 } \)
6.
(c)
1
7.
(c)
1
8.
(a)
1/8
9.
(d)
1/3
10.
(d)
5
11.
(a)
1
12.
(b)
3
13.
(c)
\(5\sqrt { 5 } \)
14.
(a)
0
15.
(a)
1
16.
(b)
9
17.
(b)
b
18.
(d)
\(\frac { \left( \sqrt { 5 } -\sqrt { 2 } \right) }{ 3 } \)
19.
(b)
3.146
20.
(d)
\(-\frac { 1 }{ \sqrt { 2 } } \)
21.
(c)
\(4\sqrt { 6 } \)
22.
(b)
9/2
23.
(b)
\(\frac { 25 }{ 7 } \)
24.
(d)
negative and rational
25.
(b)
positive and rational
26.
(a)
\(\sqrt { 16 } -4\)
27.
(c)
\({ a }^{ 2 }-b\)
28.
(c)
\(2\sqrt { a } \)
29.
(b)
\(\frac { 5 }{ 9 } \)
30.
(c)
3
31.
(c)
0.750 7500 75000...
32.
(c)
an irrational number
33.
(d)
non-terminating non-recurring
34.
(d)
3.101 1001 10001...
35.
(a)
\(\sqrt { 23 } \)
36.
(d)
0.501 5001 50001...
37.
(d)
between 5.3777 and 5.3778
38.
(a)
successive magnification
39.
(d)
0.401 4001 40001 4...
40.
(d)
0.853 853 853....
41.
(c)
non terminating and non repeating
42.
(c)
a rational number
43.
(b)
0.056
44.
(d)
real
45.
(c)
5/6 and 7/6
46.
(c)
-3/10
47.
(c)
1.6
48.
(a)
0
49.
(c)
a real number
50.
(d)
0
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